Abstract
This paper explores De Finetti’s generalized versions of Dutch Book and Accuracy Domination theorems. Following proposals due to Jeff Paris, we construe these as underpinning a generalized probabilism appropriate to belief states against either a classical or a non-classical background. Both results are straightforward corollaries of the separating hyperplane theorem; their geometrical relationship is examined. It is shown that each point of Accuracy Domination for b induces a Dutch Book on b; but Dutch Books may need to be ‘scaled’ in order to find a point of Accuracy-Domination. Finally, diachronic Dutch Book defences of conditionalization are examined in the general setting. The formulation and limitations of the generalized conditionalization this delivers are examined.
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